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Table of contents
1 Introduction (en français)
1.1 Un modèle structurel risque-neutre pour la valorisation et la couverture de produits dérivés sur l’électricité
1.2 Un algorithme probabiliste pour la résolution de problèmes de commutation optimale
en grande dimension
1.3 Un algorithme numérique pour la résolution des équations de HJB totalement non-linéaires via EDSRs à sauts négatifs
2 Introduction (in English)
2.1 A structural risk neutral model for pricing and hedging electricity derivatives
2.2 A probabilistic numerical method for optimal multiple switching problem in high dimension
2.3 A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
3 A structural risk-neutral model for pricing and hedging power derivatives
3.1 Introduction
3.2 Electricity spot market model
3.2.1 Spot model
3.2.2 Estimation and backtesting
3.3 Pricing and hedging
3.3.1 Model for capacity, demand and fuel prices
3.3.2 Choice of pricing measure
3.3.3 Electricity futures
3.3.4 Pricing formulae
3.3.5 Hedging derivatives
3.4 Numerical results
3.4.1 Explicit model for capacities and demand
3.4.2 Computing the Conditional Expectation of Scarcity Function
3.4.3 Pricing and Hedging
3.5 Conclusion
3.6 Appendices
3.6.1 Dataset
3.6.2 Proofs
3.6.3 Algorithms
4 A probabilistic numerical method for optimal multiple switching problem in high dimension
4.1 Introduction
4.2 Optimal switching problem
4.2.1 Formulation
4.2.2 Assumptions
4.2.3 Outline of the solution
4.3 Numerical approximation and convergence analysis
4.3.1 Approximations
4.3.2 Convergence analysis
4.4 Complexity analysis and memory reduction
4.4.1 Complexity
4.4.2 General memory reduction method
4.5 Application to investment in electricity generation
4.5.1 Modeling
4.5.2 Numerical results
4.6 Conclusion
4.7 Appendices
4.7.1 Lp convergence speed of empirical mean
4.7.2 Positivity of cointegrated geometric Brownian motions
4.7.3 No jump measure for diffusion-based discontinuities
4.7.4 Empirical confidence intervals
4.7.5 Graphical representation of random processes
5 A numerical algorithm for fully nonlinear HJB equations via BSDEs with nonpositive jumps
5.1 Introduction
5.2 Time discretization
5.2.1 The forward regime switching process
5.2.2 Discretely jump-constrained BSDE
5.2.3 Convergence of discretely jump-constrained BSDE
5.2.4 Approximation scheme for jump-constrained BSDE and stochastic control problem
5.3 Approximation of conditional expectations
5.3.1 Localizations
5.3.2 Projections
5.4 Applications
5.4.1 Linear Quadratic stochastic control problem
5.4.2 Uncertain volatility/correlation model
5.4.3 Comparisons with [62]
5.5 Conclusion
Bibliography
